Why is this image not staying in place when using the UV Project modifier?
Here is a setting with 3 empties as projectors on a cube.


Face: pointing to the cube's face. Z of the empty is opposite to the face
Right: pointing to the cube's right par. Z of the empty is going right (opposite again)
Left: same principle


Use "override image" option in the modifier.

Each empty has been moved and scaled to fit the image texture at the wanted location.

edit as unclear. If you don't use override option, just make so the empty are well oriented (minus Z pointing to the wanted face). It supposes that you have placed the UV map correctly before using the modifier.





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